This invention relates to crystal resonators and more particularly to structure for mounting and supporting the crystal of a crystal resonator in a manner to reduce acceleration sensitivity.
Quartz crystal resonators have been in use for years as precise frequency sources in crystal-controlled oscillators. Such resonators typically consist of a disc-shaped quartz crystal supported at its perimeter by some type of mounting structure. Examples of prior art resonators are described in Besson, R. et al, "Design of Bulk Wave Quartz Resonator Insensitive to Acceleration", Proc. 33rd Annual Symposium on Frequency Control (1979) and Aubrey, J. P., et al, "Analyse des Mecanismes de Sensibilites Accelerometrique et Barometrique des Resonateurs a Quartz de Type QAS", Fer Forum Europeen Temps-Frequence- 1987.
Even though quartz crystal resonators exhibit a high degree of accuracy and stability, when the resonators are subject to acceleration, for example because of vibration, shock, gravity, etc., frequency shifts occur and this, of course, gives rise to error. Frequency shifts are caused by stress patterns set up in the crystal as a result of the crystal reacting against its mounting structure (or the mounting structure applying a force to the crystal) under acceleration. The stress patterns interact with the active region of vibration (see copending U.S. patent application, Ser. No. 07/103,670, filed Oct. 2, 1987) of a thickness shear vibration mode crystal to shift the resonant frequency.
Mounting structure presently used to mount resonator crystals is shown in FIGS. 1A and 1B. With this structure, metal strips 4 hold a crystal 8 at two or more (four shown in the drawing) locations around the perimeter of the crystal. Because of the rigidity of the strips 4 in the lateral or sideways direction, and the flexibility of the strips in the frontward and rearward directions, when a force is applied to the crystal 8 in the plane of the crystal (for example, a body force caused by gravity or acceleration) as shown in FIG. 1B, the strips and crystal bend (exaggerated) as shown. This bending of the crystal 8 affects how the strips share the load of the crystal. It is the load sharing that gives rise to stress patterns in the crystal which interact with the active region of vibration to shift the resonant mode frequency.
FIGS. 2A through 2C show the three in-plane stress patterns created in the crystal 8 when it is subjected to the body force shown in FIG. 1B acting in the -x direction. FIG. 2A shows contours of extensional stress T.sub.xx (compression on the right side of the crystal 8 because strip 4a is pressing against the crystal and tension on the left side because strip 4b is pulling away from the crystal). The active region of vibration or mode 12 is shown as a dashed line. If the mode is as shown in FIG. 2A, i.e., at the geometric center, there are as many + (tension) contour lines as - (compression) contour lines encompassed by the mode, so the average stress in the mode is zero and there will be no effect on the frequency. If, however, the mode is off-center in the +x
direction, there will be more + (positive) contour lines than - (negative) contour lines encompassed by the mode and there will be a frequency shift because the average stress is + (positive). Conversely, if the mode is off-center in the -x direction, the opposite net stress occurs and the frequency shift is opposite.
FIG. 2B shows the extensional stress T.sub.zz for force acting the same as in FIG. 2A, i.e., in the -x direction. This stress is produced primarily by strips 4c and 4d acting on the crystal 8. Once again, if the mode 12 (shown as a dashed line in FIG. 2B) is centered, the average stress is zero and there is no frequency shift. If the mode is off-center in the +x direction, there will be a frequency shift because the average stress in the active region of vibration becomes negative--because more negative side contour lines are encompassed by the mode than positive side contour lines. The converse applies for a mode off-center in the -x direction.
FIG. 2C shows the third in-plane stress, which is shear stress T.sub.xz, produced primarily by strips 4c and 4d acting against the crystal 8. The contour lines for this stress are at right angles to the contour lines of FIGS. 2A and 2B. Thus, if the mode 12 is off-center in either the + or - z direction, the average stress will not be zero and there will be a frequency shift.
Note from FIGS. 2A through 2C that the mode cannot be off-center in either the x or z direction without encompassing more positive than negative contour lines, or vice-versa, of one of the stresses T.sub.xx and T.sub.zz, or T.sub.xz respectively. If the mode is off-center due to processing imperfections, there will be a frequency shift. Also, if the mounts are not perfectly symmetric in placement or bending rigidity, then even with the mode in the center, there will be frequency shift because the stress patterns will not be perfectly centered.
There are three other stresses, T.sub.yy, T.sub.xy, and T.sub.zy, for gravity acting in the -x direction but these are much smaller and their contribution to a frequency shift much less. Nevertheless, these stresses can affect the repeatability and accuracy of the resonator.
With the stress patterns as shown in FIGS. 2A-2C, the active region of vibration cannot be located off center in either the x direction or z direction without there being a nonzero average stress thus causing a frequency shift. This situation, however, is used to advantage in the aforecited copending patent application since movement of the active region of vibration so that it crosses contour lines can yield improved acceleration sensitivity, for example, in the x direction. Thus, so long as the acceleration takes place in the x direction, improved acceleration sensitivity is achieved. However, if acceleration of the crystal is likely to occur also, for example, in the z direction, then it may be necessary to further move the active region of vibration, for instance, in the z direction, to obtain improved acceleration sensitivity in that direction. Unfortunately, in most circumstances, this means that stress contour lines in the crystal for x direction acceleration will have been crossed by movement of the active region of vibration to accommodate the z direction acceleration and thus an undesirable frequency shift for x direction acceleration may be introduced. It would be desireable to be able to move the active region of vibration to improve sensitivity for acceleration in one direction without affecting the sensitivity to acceleration in another direction.